Note that this is not recommended to do, unless you absolutely have to. Linux Mint comes pre-installed with Adobe Flash, and at the very least will work with Firefox. Using the latest version of Adobe Flash from their website, instead of the version provided by Linux Mint, risks you getting distorted videos (wrong colours) on websites such as Youtube amongst other known issues. As such, Linux Mint has stuck to a somewhat older version on which these issues are not present.

But if you need it for some website, go ahead. Just be aware that when you do get wrong colours in videos (which doesn't happen on all graphics cards), this is the cause.